A train car with mass = 609 kg is moving to the right with a speed of = 7.7 m/s and collides with a second train car. The two cars latch together during the collision and then move off to the right at = 4.6 m/s.
a. What is the initial momentum of the first train car?
b. What is the mass of the second train car?
c. What is the change in kinetic energy of the two train system during the collision?

a. 4689.3 kgm/s b 410.41 kg c. -7268.45 J

Explanation:

a. The initial momentum of the first train car is given by p₁ = m₁v₁ where m₁ = 609 kg and v₁ = 7.7 m/s. So p₁ = m₁v₁ = 609 kg × 7.7 m/s = 4689.3 kgm/s

b. From the law of conservation of momentum,

m₁v₁ + m₂v₂ = (m₁ + m₂)v where m₂ = mass of second train car, v₂ = speed of second train car = 0 m/s (since it is stationary relative to the first train car )and v = velocity during collision = 4.6 m/s

m₁v₁ + m₂v₂ = (m₁ + m₂)v

609 kg × 7.7 m/s + m₂ × 0 = (609 + m₂)4.6

4689.3 + 0 = 2801.4 + 4.6m₂

4689.3 - 2801.4 = 4.6m₂

1887.9 = 4.6m₂

m₂ = 1887.9/4.6 = 410.41 kg

c. The kinetic energy change of the two train system ΔK = K₂ - K₁ where K₂ = final kinetic energy of two train system and K₁ = initial kinetic energy of two train system.

K₁ = 1/2m₁v₁² + 1/2m₂v₂² = 1/2 × 609 × 7.7² + 1/2 × 410.41 × 0² = 18053.81 J + 0 J = 18053.81 J

K₂ = 1/2(m₁ + m₂)v² = 1/2 (609 + 410.41)4.6² =1/2 × 1019.41 × 4.6² = 10785.36 J.

So, ΔK = K₂ - K₁ = 10785.36 J - 18053.81 J = -7268.45 J

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air exerts forces on falling objects near earth’s surface.

explanation:

the term 'free falls' refer to object that are falling towards the earth, in a situation in which gravity is the only force acting on the object.

for an object in free fall, the acceleration is constant (g, the gravitational acceleration), and so the velocity of the object constantly increases.

for objects near earth's surface, there is always another force acting on the object: the resistance due to the air. this force is opposed to the direction of fall of the object, and it is proportional to the velocity of the object, so as the object falls down, this force increases up to a point when it balances the force of gravity, and the object continues its motion at constant velocity (called terminal velocity). since in this case gravity is not the only force acting on the object, we are not in a situation of free fall.